A movie buff owns movies on DVD and on Blu-ray...

Hi LUANDATO,

We're told that a movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2 and that if she buys 6 more Blu-ray movies, then that ratio would change to 11:4. We're asked for the original total number of movies in her library BEFORE the extra purchase. This question is based on ratio rules and can be approached in a number of different ways.

To start, since you can't have a 'fraction' of a DVD, the original number of DVDs will be a multiple of 7 and the original number of Blu-rays will be an equivalent multiple of 2...

For example:
7 DVDs and 2 Blu-rays; 9 total
14 DVDs and 4 Blu-rays; 18total
21 DVDs and 6 Blu-rays; 27 total

By extension, the TOTAL number of DVDs and Blu-rays will be a multiple of 9. At this point, you can actually stop working - there's only one answer that's a multiple of 9. The GMAT won't often make it this easy on you to answer this type of question, so some additional math work would likely be required.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 6 more Blu-ray movies, that ratio would change to 11:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?

A. 22
B. 28
C. 77
D. 99
E. 105

We can let the original number of DVD and Blu-ray she owns be 7x and 2x, respectively. Thus we can create the equation:

7x/(2x + 6) = 11/4

4(7x) = 11(2x + 6)

28x = 22x + 66

6x = 66

x = 11

She originally had 7x + 2x = 9x movies; therefore, she owned 9(11) = 99movies.

Answer: D